The term " equitability " was introduced by Reshef et al. in ref. 1 to describe measures of statistical dependence that " give similar scores to equally noisy relationships of different types. " Their paper also introduced a new statistic, the " maximal information coefficient " (MIC), that was said to satisfy this equitability criterion. There has since been much interest in MIC, due primarily...

How should one quantify the strength of association between two random variables without bias for relationships of a specific form? Despite its conceptual simplicity, this notion of statistical "equitability" has yet to receive a definitive mathematical formalization. Here we argue that equitability is properly formalized by a self-consistency condition closely related to Data Processing Inequa...

In exploratory data analysis, we are often interested in identifying promising pairwise associations for further analysis while filtering out weaker ones. This can be accomplished by computing a measure of dependence on all variable pairs and examining the highest-scoring pairs, provided the measure of dependence used assigns similar scores to equally noisy relationships of different types. Thi...

Although we appreciate Kinney and Atwal’s interest in equitability and maximal information coefficient (MIC), we believe they misrepresent our work. We highlight a few of our main objections below. Regarding our original paper (1), Kinney and Atwal (2) state “MIC is said to satisfy not just the heuristic notion of equitability, but also the mathematical criterion of R equitability,” the latter ...

There are many applications across a broad range of business problem domains in which equity is a concern and many well-known operational research (OR) problems such as knapsack, scheduling or assignment problems have been considered from an equity perspective. This shows that equity is both a technically interesting concept and a substantial practical concern. In this paper we review the opera...

The concept of statistical " equitability " plays a central role in the 2011 paper by Reshef et al. (1). Formalizing equitability first requires formalizing the notion of a " noisy functional relationship, " that is, a relationship between two real variables, X and Y, having the form Y = f ðXÞ + η; where f is a function and η is a noise term. Whether a dependence measure satisfies equi-tability...

In exploratory data analysis, we are often interested in identifying promising pairwise associations for further analysis while filtering out weaker, less interesting ones. This can be accomplished by computing a measure of dependence on all possible variable pairs and examining the highest-scoring pairs, provided the measure of dependence used assigns similar scores to equally noisy relationsh...

The maximal information coefficient (MIC) is a tool for finding the strongest pairwise relationships in a data set with many variables [1]. MIC is useful because it gives similar scores to equally noisy relationships of different types. This property, called equitability, is important for analyzing high-dimensional data sets. Here we formalize the theory behind both equitability and MIC in the ...